Problem: Michael is 3 times as old as Kevin. Fifteen years ago, Michael was 8 times as old as Kevin. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Kevin. Let Michael's current age be $m$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $m = 3k$ Fifteen years ago, Michael was $m - 15$ years old, and Kevin was $k - 15$ years old. The information in the second sentence can be expressed in the following equation: $m - 15 = 8(k - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = 3k$ . Substituting this into our second equation, we get: $3k$ $-$ $15 = 8(k - 15)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $3 k - 15 = 8 k - 120$ Solving for $k$ , we get: $5 k = 105.$ $k = 21$.